FIA NLS Models: Biomass Growth vs. Stand Age
JAH
2023-07-12
Background
This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data with an intermediate maximum (i.e., “hump” shaped) curve. As in our models of biomass growth vs. biomass, we use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement intervals (FIA re-measurement period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): the productivity trend, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.
Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {StdAge_{t1}^2}\) in equal-sample sized plot biomass bins (n=20 where applicable, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is done to determine the best fitting models, considering the inclusion of \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest). Thus, the following two models are considered:
model 1: simple (tau) model \(G = (1 + (yr-1990) \cdot tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 3: model \(G = (1 + (yr-1990) \cdot tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6838 2148.3
## 2 6837 2052.6 1 95.655 318.61 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 27051.67
## 2 2 26741.98##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.31226 0.17582 1.776 0.075784 .
## alpha 0.63852 0.03351 19.054 < 2e-16 ***
## a 0.00000 1.60068 0.000 1.000000
## b 3.43281 1.59386 2.154 0.031294 *
## c 34.47438 1.75397 19.655 < 2e-16 ***
## d 2.54310 0.73279 3.470 0.000523 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5479 on 6837 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (41 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.## Warning: Removed 23 rows containing missing values (`geom_point()`).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18526 8253.7
## 2 18525 7741.2 1 512.48 1226.4 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 68451.26
## 2 2 67265.37##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.39928 0.17845 7.841 4.70e-15 ***
## alpha 0.82379 0.02151 38.294 < 2e-16 ***
## a 1.10879 0.26512 4.182 2.90e-05 ***
## b 1.24528 0.24934 4.994 5.96e-07 ***
## c 22.86693 0.96168 23.778 < 2e-16 ***
## d 1.78699 0.29232 6.113 9.97e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6464 on 18525 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (4154 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 1843 rows containing missing values (`geom_point()`).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6924 2689.6
## 2 6923 2569.8 1 119.77 322.64 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 30842.27
## 2 2 30528.64##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.44591 0.15003 -2.972 0.00297 **
## alpha 0.76139 0.03963 19.212 < 2e-16 ***
## a 0.00000 30.61728 0.000 1.00000
## b 4.40702 30.60200 0.144 0.88550
## c 38.99102 8.01905 4.862 1.19e-06 ***
## d 2.81200 10.68362 0.263 0.79240
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6093 on 6923 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (378 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 25 rows containing missing values (`geom_point()`).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4757 1856.5
## 2 4756 1762.7 1 93.856 253.24 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 19612.03
## 2 2 19366.98##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.21663 0.23614 0.917 0.359
## alpha 0.77245 0.04446 17.373 < 2e-16 ***
## a 2.57655 0.18696 13.781 < 2e-16 ***
## b 0.81266 0.14950 5.436 5.73e-08 ***
## c 52.88239 2.44781 21.604 < 2e-16 ***
## d 0.77801 0.14915 5.216 1.90e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6088 on 4756 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1084 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 501 rows containing missing values (`geom_point()`).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8449 3574.8
## 2 8448 3491.5 1 83.323 201.61 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 35000.76
## 2 2 34803.38##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.19097 0.14827 -1.288 0.1978
## alpha 0.62818 0.04177 15.037 < 2e-16 ***
## a 1.68617 1.42899 1.180 0.2380
## b 1.97015 1.41691 1.390 0.1644
## c 28.57096 4.30586 6.635 3.44e-11 ***
## d 1.65615 0.92012 1.800 0.0719 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6429 on 8448 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1552 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 616 rows containing missing values (`geom_point()`).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12080 5704.0
## 2 12079 4963.9 1 740.08 1800.9 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 60303.17
## 2 2 58625.69##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.54440 0.18218 8.477 <2e-16 ***
## alpha 0.90652 0.01895 47.844 <2e-16 ***
## a 2.98244 0.12403 24.045 <2e-16 ***
## b 1.91633 0.09835 19.485 <2e-16 ***
## c 17.48671 0.48145 36.321 <2e-16 ***
## d 0.98628 0.06672 14.783 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6411 on 12079 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (759 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 96 rows containing missing values (`geom_point()`).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12420 8127.3
## 2 12419 7172.3 1 954.97 1653.5 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 62939.2
## 2 2 61388.1##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.65220 0.21855 7.56 4.32e-14 ***
## alpha 0.89704 0.01912 46.91 < 2e-16 ***
## a 2.76534 0.10479 26.39 < 2e-16 ***
## b 1.87484 0.09535 19.66 < 2e-16 ***
## c 16.11438 0.43598 36.96 < 2e-16 ***
## d 0.81297 0.04623 17.58 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.76 on 12419 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (742 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 129 rows containing missing values (`geom_point()`).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1271 759.14
## 2 1270 714.87 1 44.271 78.649 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6448.107
## 2 2 6373.437##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.85607 0.72485 1.181 0.237812
## alpha 0.78091 0.07943 9.831 < 2e-16 ***
## a 3.41726 0.47753 7.156 1.4e-12 ***
## b 1.74467 0.45124 3.866 0.000116 ***
## c 18.45899 2.24438 8.225 4.8e-16 ***
## d 0.69423 0.18461 3.761 0.000177 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7503 on 1270 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (68 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 17 rows containing missing values (`geom_point()`).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1737 622.69
## 2 1736 616.67 1 6.024 16.958 4e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6711.617
## 2 2 6696.682##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.6255 0.4418 1.416 0.1570
## alpha 0.4154 0.0965 4.304 1.77e-05 ***
## a 1.8585 1.0940 1.699 0.0895 .
## b 0.8413 1.0662 0.789 0.4302
## c 42.8805 4.5384 9.448 < 2e-16 ***
## d 1.1374 1.0631 1.070 0.2848
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.596 on 1736 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (548 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 246 rows containing missing values (`geom_point()`).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 670 743.09
## 2 669 721.23 1 21.866 20.282 7.883e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3193.464
## 2 2 3175.304##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.1668 1.3234 0.882 0.378260
## alpha 0.7372 0.1466 5.028 6.37e-07 ***
## a 0.7819 0.6694 1.168 0.243203
## b 2.4068 0.8155 2.951 0.003275 **
## c 18.3942 1.9567 9.401 < 2e-16 ***
## d 1.2802 0.3703 3.457 0.000581 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.038 on 669 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (39 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 28 rows containing missing values (`geom_point()`).
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
411 - Everglades
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6752 1843.1
## 2 6751 1736.0 1 107.05 416.31 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25591.01
## 2 2 25188.68##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.91157 0.21485 4.243 2.24e-05 ***
## alpha 0.63278 0.02885 21.931 < 2e-16 ***
## a 1.85659 0.47443 3.913 9.19e-05 ***
## b 1.21316 0.45513 2.666 0.007705 **
## c 32.57864 2.02236 16.109 < 2e-16 ***
## d 1.58600 0.45499 3.486 0.000494 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5071 on 6751 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (21 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 9 rows containing missing values (`geom_point()`).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7755 3828.1
## 2 7754 3733.2 1 94.905 197.12 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36463.27
## 2 2 36270.47##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.97063 0.23310 4.164 3.16e-05 ***
## alpha 0.82315 0.05549 14.835 < 2e-16 ***
## a 2.61737 0.22420 11.674 < 2e-16 ***
## b 1.26213 0.20978 6.016 1.86e-09 ***
## c 31.41373 4.34802 7.225 5.49e-13 ***
## d 0.92534 0.23823 3.884 0.000103 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6939 on 7754 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (426 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 20 rows containing missing values (`geom_point()`).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 882 523.43
## 2 881 505.66 1 17.765 30.951 3.51e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3696.088
## 2 2 3667.461##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.6254 1.8187 1.993 0.046522 *
## alpha 0.9031 0.1494 6.045 2.20e-09 ***
## a 1.4214 0.3248 4.376 1.35e-05 ***
## b 0.9469 0.3297 2.872 0.004178 **
## c 32.2962 2.9490 10.951 < 2e-16 ***
## d 0.4015 0.1103 3.640 0.000289 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7576 on 881 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (6 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 3 rows containing missing values (`geom_point()`).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 952 508.31
## 2 951 472.57 1 35.732 71.906 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4009.792
## 2 2 3942.037##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 4.49267 2.22922 2.015 0.04415 *
## alpha 0.93086 0.09812 9.487 < 2e-16 ***
## a 1.41548 0.34868 4.060 5.32e-05 ***
## b 0.90555 0.30172 3.001 0.00276 **
## c 24.41902 1.76448 13.839 < 2e-16 ***
## d 0.33959 0.08496 3.997 6.91e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7049 on 951 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (52 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 4 rows containing missing values (`geom_point()`).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3217 2988.6
## 2 3216 2870.6 1 118.03 132.23 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17568.85
## 2 2 17441.02##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.56033 0.30652 -5.090 3.78e-07 ***
## alpha 0.96775 0.07628 12.686 < 2e-16 ***
## a 5.95368 0.57338 10.384 < 2e-16 ***
## b 4.31980 0.84430 5.116 3.30e-07 ***
## c 35.17210 1.72271 20.417 < 2e-16 ***
## d 0.32134 0.05981 5.373 8.32e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9448 on 3216 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (81 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 38 rows containing missing values (`geom_point()`).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 1618.2
## 2 1690 1593.0 1 25.215 26.752 2.589e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8793.291
## 2 2 8768.655##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.4597 0.2437 -10.093 < 2e-16 ***
## alpha 0.6951 0.1251 5.558 3.16e-08 ***
## a 0.0000 4.5132 0.000 1.0000
## b 8.0203 4.5315 1.770 0.0769 .
## c 47.0468 7.6497 6.150 9.64e-10 ***
## d 2.6658 1.1090 2.404 0.0163 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9709 on 1690 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (297 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 139 rows containing missing values (`geom_point()`).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 360 174.32
## 2 359 168.10 1 6.2251 13.295 0.0003055 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1014.707
## 2 2 1003.435##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.4926 0.3002 -8.304 2.08e-15 ***
## alpha 0.5805 0.1477 3.931 0.000101 ***
## a 0.0000 5.0588 0.000 1.000000
## b 3.3501 5.1051 0.656 0.512096
## c 61.8680 17.6811 3.499 0.000526 ***
## d 2.0796 2.2905 0.908 0.364527
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6843 on 359 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1723 1595.8
## 2 1722 1539.2 1 56.677 63.41 3.022e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 5203.597
## 2 2 5143.110##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.78590 0.63025 -1.247 0.212583
## alpha 0.60002 0.06600 9.091 < 2e-16 ***
## a 0.05448 0.69849 0.078 0.937841
## b 1.87371 0.74000 2.532 0.011429 *
## c 48.95939 3.63220 13.479 < 2e-16 ***
## d 1.99791 0.57426 3.479 0.000516 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9454 on 1722 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (29 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 14 rows containing missing values (`geom_point()`).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2510 2063.2
## 2 2509 1942.9 1 120.36 155.43 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9308.899
## 2 2 9159.737## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df2$Code == "M332", , value =
## structure(list(: provided 26 variables to replace 25 variables##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.47206 0.59179 -0.798 0.425
## alpha 0.83144 0.05826 14.270 < 2e-16 ***
## a 0.00000 0.34184 0.000 1.000
## b 2.48370 0.48494 5.122 3.26e-07 ***
## c 61.74217 4.48508 13.766 < 2e-16 ***
## d 2.29043 0.30910 7.410 1.72e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.88 on 2509 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (106 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 55 rows containing missing values (`geom_point()`).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1687 947.40
## 2 1686 857.14 1 90.266 177.55 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6940.909
## 2 2 6773.494##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.48912 0.66184 -0.739 0.46
## alpha 0.87691 0.05808 15.099 < 2e-16 ***
## a 1.00833 0.22997 4.385 1.23e-05 ***
## b 3.25634 0.55305 5.888 4.71e-09 ***
## c 47.89490 1.79385 26.699 < 2e-16 ***
## d 1.35417 0.09350 14.484 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.713 on 1686 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (66 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Removed 34 rows containing missing values (`geom_point()`).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 342 271.03
## 2 341 280.93 1 -9.9002 -12.017 1
## model AIC
## 1 1 1081.021
## 2 2 1095.471##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a +
## b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.347488 0.730018 -1.846 0.06578 .
## a 1.631370 0.322270 5.062 6.79e-07 ***
## b 12.311276 10.354016 1.189 0.23525
## c 56.399282 0.345131 163.414 < 2e-16 ***
## d 0.015805 0.005956 2.653 0.00834 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8902 on 342 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (104 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.## Warning: Removed 48 rows containing missing values (`geom_point()`).## Warning: Removed 1 rows containing missing values (`geom_segment()`).
plotting 2
## Warning: Removed 1 rows containing missing values (`geom_segment()`).
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 2 |
| 212 | Laurentian Mixed Forest | 2 |
| 221 | Eastern Broadleaf Forest | 2 |
| 222 | Midwest Broadleaf Forest | 2 |
| 223 | Central Interior Broadleaf Forest | 2 |
| 231 | Southeastern Mixed Forest | 2 |
| 232 | Outer Coastal Plain Mixed Forest | 2 |
| 234 | Lower Mississippi Riverine Forest | 2 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 2 |
| 255 | Prairie Parkland (Subtropical) | 2 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2 |
| M223 | Ozark Broadleaf Forest Meadow | 2 |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 2 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M334 | Black Hills Coniferous Forest | 1 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6884 | 2879 | 0.3122552 | 0.0309139 | -0.0324135 | 0.6569239 | 0.6385218 | 0.0011229 | 0.5728311 | 0.7042125 | 0.0000000 | -3.1378297 | 3.1378297 | 3.4328070 | 0.3083369 | 6.557277 | 34.47438 | 31.03604 | 37.91271 | 2.5431020 | 1.1065977 | 3.9796063 |
| 212 | Laurentian Mixed Forest | east | 22685 | 9493 | 1.3992776 | 0.0318451 | 1.0494953 | 1.7490599 | 0.8237918 | 0.0004628 | 0.7816260 | 0.8659577 | 1.1087858 | 0.5891184 | 1.6284531 | 1.2452806 | 0.7565452 | 1.734016 | 22.86693 | 20.98194 | 24.75192 | 1.7869885 | 1.2140129 | 2.3599640 |
| 221 | Eastern Broadleaf Forest | east | 7307 | 3560 | -0.4459077 | 0.0225082 | -0.7400075 | -0.1518079 | 0.7613862 | 0.0015706 | 0.6836980 | 0.8390745 | 0.0000000 | -60.0192561 | 60.0192561 | 4.4070188 | -55.5822911 | 64.396329 | 38.99102 | 23.27122 | 54.71082 | 2.8120005 | -18.1311648 | 23.7551659 |
| 222 | Midwest Broadleaf Forest | east | 5846 | 2589 | 0.2166263 | 0.0557622 | -0.2463179 | 0.6795706 | 0.7724515 | 0.0019769 | 0.6852858 | 0.8596172 | 2.5765512 | 2.2100221 | 2.9430802 | 0.8126565 | 0.5195614 | 1.105752 | 52.88239 | 48.08354 | 57.68123 | 0.7780129 | 0.4856186 | 1.0704073 |
| 223 | Central Interior Broadleaf Forest | east | 10006 | 3860 | -0.1909729 | 0.0219849 | -0.4816243 | 0.0996784 | 0.6281816 | 0.0017451 | 0.5462934 | 0.7100697 | 1.6861654 | -1.1150130 | 4.4873439 | 1.9701492 | -0.8073439 | 4.747642 | 28.57096 | 20.13043 | 37.01150 | 1.6561479 | -0.1475169 | 3.4598128 |
| 231 | Southeastern Mixed Forest | east | 12844 | 5935 | 1.5444034 | 0.0331912 | 1.1872927 | 1.9015141 | 0.9065157 | 0.0003590 | 0.8693760 | 0.9436555 | 2.9824352 | 2.7393098 | 3.2255606 | 1.9163298 | 1.7235497 | 2.109110 | 17.48671 | 16.54300 | 18.43042 | 0.9862759 | 0.8554977 | 1.1170541 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13167 | 6463 | 1.6522029 | 0.0477639 | 1.2238119 | 2.0805939 | 0.8970390 | 0.0003657 | 0.8595565 | 0.9345215 | 2.7653363 | 2.5599380 | 2.9707346 | 1.8748420 | 1.6879393 | 2.061745 | 16.11438 | 15.25979 | 16.96897 | 0.8129738 | 0.7223488 | 0.9035987 |
| 234 | Lower Mississippi Riverine Forest | east | 1344 | 759 | 0.8560691 | 0.5254062 | -0.5659643 | 2.2781025 | 0.7809110 | 0.0063094 | 0.6250795 | 0.9367426 | 3.4172574 | 2.4804182 | 4.3540967 | 1.7446654 | 0.8594056 | 2.629925 | 18.45899 | 14.05589 | 22.86210 | 0.6942325 | 0.3320557 | 1.0564093 |
| 242 | Pacific Lowland Mixed Forest | west | 85 | 85 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2290 | 903 | 0.6254893 | 0.1951663 | -0.2409806 | 1.4919592 | 0.4153713 | 0.0093131 | 0.2260938 | 0.6046489 | 1.8585086 | -0.2871227 | 4.0041398 | 0.8413334 | -1.2498538 | 2.932521 | 42.88047 | 33.97925 | 51.78170 | 1.1374160 | -0.9476629 | 3.2224949 |
| 255 | Prairie Parkland (Subtropical) | east | 714 | 318 | 1.1668247 | 1.7513681 | -1.4316784 | 3.7653277 | 0.7371667 | 0.0214935 | 0.4493024 | 1.0250309 | 0.7818704 | -0.5324699 | 2.0962108 | 2.4067541 | 0.8055229 | 4.007985 | 18.39423 | 14.55217 | 22.23628 | 1.2801691 | 0.5530109 | 2.0073273 |
| 261 | California Coastal Chaparral Forest and Shrub | west | 26 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | west | 159 | 157 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | west | 218 | 218 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | west | 232 | 128 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6778 | 3008 | 0.9115699 | 0.0461617 | 0.4903907 | 1.3327492 | 0.6327756 | 0.0008325 | 0.5762141 | 0.6893371 | 1.8565947 | 0.9265603 | 2.7866291 | 1.2131629 | 0.3209625 | 2.105363 | 32.57864 | 28.61417 | 36.54311 | 1.5860017 | 0.6940825 | 2.4779210 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8186 | 3765 | 0.9706339 | 0.0543361 | 0.5136927 | 1.4275750 | 0.8231535 | 0.0030790 | 0.7143811 | 0.9319259 | 2.6173655 | 2.1778674 | 3.0568635 | 1.2621315 | 0.8508994 | 1.673364 | 31.41373 | 22.89045 | 39.93702 | 0.9253407 | 0.4583535 | 1.3923278 |
| M223 | Ozark Broadleaf Forest Meadow | east | 893 | 348 | 3.6253706 | 3.3075234 | 0.0559592 | 7.1947820 | 0.9031479 | NA | 0.6099409 | 1.1963549 | 1.4213702 | 0.7839099 | 2.0588306 | 0.9469136 | 0.2997905 | 1.594037 | 32.29616 | 26.50819 | 38.08413 | 0.4015031 | 0.1850123 | 0.6179939 |
| M231 | Ouachita Mixed Forest | east | 1009 | 496 | 4.4926690 | 4.9694290 | 0.1179072 | 8.8674308 | 0.9308607 | 0.0096279 | 0.7383007 | 1.1234207 | 1.4154833 | 0.7312187 | 2.0997480 | 0.9055507 | 0.3134288 | 1.497673 | 24.41902 | 20.95630 | 27.88174 | 0.3395869 | 0.1728615 | 0.5063123 |
| M242 | Cascade Mixed Forest | west | 3303 | 3286 | -1.5603333 | 0.0939549 | -2.1613288 | -0.9593377 | 0.9677509 | 0.0058191 | 0.8181824 | 1.1173195 | 5.9536792 | 4.8294557 | 7.0779027 | 4.3198009 | 2.6643712 | 5.975231 | 35.17210 | 31.79437 | 38.54982 | 0.3213441 | 0.2040698 | 0.4386184 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | west | 1993 | 1828 | -2.4597236 | 0.0593881 | -2.9377029 | -1.9817442 | 0.6951360 | 0.0156415 | 0.4498356 | 0.9404364 | 0.0000000 | -8.8521409 | 8.8521409 | 8.0202996 | -0.8676141 | 16.908213 | 47.04680 | 32.04300 | 62.05061 | 2.6657677 | 0.4905137 | 4.8410218 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | west | 367 | 367 | -2.4926099 | 0.0901117 | -3.0829541 | -1.9022657 | 0.5805357 | 0.0218076 | 0.2901208 | 0.8709505 | 0.0000000 | -9.9485137 | 9.9485137 | 3.3501094 | -6.6895011 | 13.389720 | 61.86805 | 27.09645 | 96.63964 | 2.0796416 | -2.4249326 | 6.5842158 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | west | 1757 | 1757 | -0.7858964 | 0.3972178 | -2.0220368 | 0.4502440 | 0.6000245 | 0.0043565 | 0.4705689 | 0.7294800 | 0.0544785 | -1.3154965 | 1.4244535 | 1.8737103 | 0.4223100 | 3.325111 | 48.95939 | 41.83541 | 56.08337 | 1.9979081 | 0.8715839 | 3.1242324 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 2621 | 2611 | -0.4720572 | 0.3502167 | -1.6325063 | 0.6883919 | 0.8314380 | 0.0033948 | 0.7171860 | 0.9456901 | 0.0000000 | -0.6703134 | 0.6703134 | 2.4836960 | 1.5327642 | 3.434628 | 61.74217 | 52.94733 | 70.53700 | 2.2904290 | 1.6843033 | 2.8965547 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 1758 | 1747 | -0.4891160 | 0.4380352 | -1.7872350 | 0.8090029 | 0.8769138 | 0.0033732 | 0.7629994 | 0.9908282 | 1.0083320 | 0.5572708 | 1.4593932 | 3.2563428 | 2.1716069 | 4.341079 | 47.89489 | 44.37648 | 51.41331 | 1.3541714 | 1.1707928 | 1.5375501 |
| M334 | Black Hills Coniferous Forest | west | 451 | 179 | -1.3474876 | 0.5329266 | -2.7833784 | 0.0884032 | NA | NA | NA | NA | 1.6313704 | 0.9974897 | 2.2652510 | 12.3112756 | -8.0542931 | 32.676844 | 56.39928 | 55.72043 | 57.07813 | 0.0158050 | 0.0040891 | 0.0275209 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
parameter variance co-variance
plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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plot alpha (biomass growth compensation effect)
plot a coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).
plot b coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).
plot c coefficient
## Warning: Removed 1 rows containing missing values (`geom_hline()`).## Warning: Removed 15 rows containing missing values (`geom_point()`).
plot d coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).